Dynamic Analysis of Geared Rotors by Finite Elements

A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.

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Coupled Bending-Torsion Vibration of Geared Rotors

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0492 ◽

1995 ◽

Author(s):

J. S. Rao ◽

J. R. Chang ◽

T. N. Shiau

Keyword(s):

Finite Element ◽

Natural Frequencies ◽

Element Model ◽

Mode Shapes ◽

Mesh Stiffness ◽

Present Program ◽

Gear Mesh ◽

Pressure Angle ◽

Torsion Vibration ◽

Gear Mesh Stiffness

Abstract A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.

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Effect of cracks and pitting defects on gear meshing

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212437104 ◽

2012 ◽

Vol 226 (11) ◽

pp. 2805-2815 ◽

Cited By ~ 38

Author(s):

Alfonso Fernandez del Rincon ◽

Fernando Viadero ◽

Miguel Iglesias ◽

Ana de-Juan ◽

Pablo Garcia ◽

...

Keyword(s):

Finite Element ◽

Computational Models ◽

Inequality Constraints ◽

Variable Stiffness ◽

Element Model ◽

Equation System ◽

Transmission Error ◽

Computational Effort ◽

Gear Mesh ◽

Non Linear

The development of vibration-based condition monitoring techniques, especially those focused on prognosis, requires the development of better computational models that enable the simulation of the vibratory behaviour of mechanical systems. Gear transmission vibrations are governed by the so-called gear mesh frequency and its harmonics, due to the variable stiffness of the meshing process. The fundamental frequency will be modulated by the appearance of defects which modify the meshing features. This study introduces an advanced model to assess the consequences of defects such as cracks and pitting on the meshing stiffness and other related parameters such as load transmission error or load sharing ratio. Meshing forces are computed by imposing the compatibility and complementarity conditions, leading to a non-linear equation system with inequality constraints. The calculation of deformations is subdivided into a global and a local type. The former is approached by a finite element model and the latter via a non-linear Herztian-based formulation. This procedure enables a reduced computational effort, in contrast to conventional finite element models with contact elements. The formulation used to include these defects is described in detail and their consequences are assessed by a quasi-static analysis of a transmission example.

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An Estimate of Mesh Stiffness and Load Sharing Ratio of a Spur Gear Pair

6th International Power Transmission and Gearing Conference: Advancing Power Transmission Into the 21st Century ◽

10.1115/detc1992-0001 ◽

1992 ◽

Author(s):

J. H. Kuang ◽

Y. T. Yang

Keyword(s):

Finite Element ◽

Element Model ◽

Spur Gear ◽

Mesh Stiffness ◽

Gear Mesh ◽

Stiffness Constant ◽

Generating Method ◽

Single Tooth ◽

Tooth Stiffness ◽

Involute Gears

Abstract A curve fitted tooth stiffness equation was developed to calculate directly the variable gear mesh stiffness. To improve the accuracy, a tooth profile generating method introduced by Litvin (1989) was employed for finite element idealization. A quadratic finite element model was employed in deriving the tooth stiffness constant at the successive positions of a single tooth as it passed through the zone of loading. The developed stiffness equation is applicable to both the standard full-depth or addendum modified involute gears. Variation of the shared loads introduced by the consideration of mesh stiffness was also investigated.

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The Static Transmission Error of Cracked Spur Gear Teeth Using FEA

Volume 6: 18th Computers in Engineering Conference ◽

10.1115/detc98/cie-5510 ◽

1998 ◽

Author(s):

Seney Sirichai ◽

Ian Howard ◽

Laurie Morgan ◽

Kian Teh

Keyword(s):

Finite Element ◽

Element Model ◽

Transmission Error ◽

Spur Gear ◽

Mesh Stiffness ◽

Element Analysis ◽

Angular Rotation ◽

Simple Strategy ◽

Static Transmission Error ◽

The Individual

Abstract This paper considers a Finite Element Model which is used to predict the torsional mesh stiffness and static transmission error of a pair of spur gears in mesh. The model involves the use of 2D plain strain elements, coupled with contact elements at the points of contact between the meshing teeth. A simple strategy of how to determine an appropriate value of the penalty parameter of the contact elements (gap element) is also presented. When gears are unloaded, a pinion and gear with perfect involute profiles, should theoretically run with zero transmission error. However, when gears with involute profiles are loaded, the individual torsional mesh stiffness of each gear changes throughout the mesh cycle, causing variations in angular rotation of the gear body and subsequent transmission error. The theoretical changes in the torsional mesh stiffness throughout the mesh cycle are developed using finite element analysis and related to the static transmission error. A 5mm through thickness tooth crack is also modelled, and the comparison of the torsional mesh stiffness and static transmission error with and without the tooth crack is discussed.

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Free and Forced Vibration Analysis of Functionally Graded Beams Using Finite Element Model Based on Refined Third-Order Theory

Lecture Notes in Mechanical Engineering - Emerging Trends in Mechanical Engineering ◽

10.1007/978-981-32-9931-3_58 ◽

2019 ◽

pp. 603-612

Author(s):

M. Altaf Khan ◽

M. Y. Yasin ◽

Mirza Shariq Beg ◽

A. H. Khan

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Forced Vibration ◽

Vibration Analysis ◽

Element Model ◽

Order Theory ◽

Functionally Graded ◽

Third Order ◽

Model Based ◽

Forced Vibration Analysis

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Hull girder: Forced vibration analysis by propeller

Ciencia y tecnología de buques ◽

10.25043/19098642.127 ◽

2016 ◽

Vol 9 (18) ◽

pp. 35

Author(s):

Franklin Domínguez

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Forced Vibration ◽

Vibration Analysis ◽

Element Model ◽

Added Mass ◽

Forced Vibrations ◽

Hull Girder ◽

Vessel Structure ◽

Forced Vibration Analysis

The non-uniform wake around the propeller generates fluctuating forces on the propulsion shaft. This article presents a methodology used for the forced vibrations analysis of hull girder due to this propeller excitation. This approach is applied to a research boat considering the propeller working in the operating range using a finite element model including all ship structures, rudder, and propulsion lines with their respective supports. Added mass and damping in all submerged elements were also considered. Vibration levels acting in the vessel structure are compared with the limits proposed by ISO 6954 (2000).

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Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

Advances in Civil Engineering ◽

10.1155/2020/1471037 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17 ◽

Cited By ~ 6

Author(s):

Trung Thanh Tran ◽

Van Ke Tran ◽

Pham Binh Le ◽

Van Minh Phung ◽

Van Thom Do ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Forced Vibration ◽

Vibration Analysis ◽

Shear Deformation Theory ◽

Laminated Composite ◽

Thermal Environments ◽

Forced Vibration Analysis ◽

Laminated Composite Shells ◽

Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

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